frequency spectrum by thyristordownloads.hindawi.com/journals/apec/1974/912162.pdfthis investigation...

Electrocomponent Science and Technology1974, Vol. 1, pp. 43-49

(C) Gordon and Breach Science Publishers Ltd.Printed in Great Britain

FREQUENCY SPECTRUM GENERATED BYTHYRISTOR CONTROL

J. K. HALL and N. C. JONES

Loughborough University of Technology, Loughborough, Leics. U.K.

(Received October 30, 1973; in final form December 19, 1973)

This paper describes the measured harmonics in the load currents of thyristor circuits and shows that with firingangle control the harmonic amplitudes decrease sharply with increasing harmonic frequency, but that they extendto very high harmonic orders of around 6000. The amplitudes of the harmonics are a maximum for a firing delayangle of around 90

Integral cycle control produces only low order harmonics and sub-harmonics.It is also shown that with firing angle control apparently random inter-harmonic noise is present and that the

harmonics fall below this noise level at frequencies of approximately 250 KHz for a switched 50 Hz waveform andfor the resistive load used. The noise amplitude decreases with increasing frequency and is a maximum with 90firing delay.

INTRODUCTION

Thyristors are now widely used for control of powerin both d.c. and a.c. circuits. The advantages ofrelatively small size, low losses and fast switchingspeeds have contributed to the vast growth inapplication since their introduction, when they werebasically a solid-state replacement for mercury-arcrectifier devices. As a result, attention has beenfocussed on the inherent problems produced bythyristor control, some of which are a perpetuationof those with mercury-arc rectifiers. These are nowgiving cause for greater concern owing to the scale ofusage. The majority of applications utilise a.c. linecommutation and only these are considered here.

The switching action of the thyristors (or triac)results in non-sinusoidal currents being drawn fromthe a.c. supply system. Harmonics and noise arethereby injected into the power supply and give rise,

to conducted interference with other electronic andcommunications equipment.2-4 Unless the apparatusis screened, radiated interference also occurs. Theeffects of interference are varied, from malfunctioningof low-level micrologic circuits and triggering of otherseparately-controlled thyristors to disturbance ofradio and T.V. reception,s The elimination of theseeffects is an important objective. Ways of suppressingthe harmonics and noise have been devised using, onthe one hand, greatly improved discrete componentsand on the other, composite devices containingwithin one component resistance, capacitance and

43

inductance.6,7 Literature on the subject tends toassume that noise is due to the high frequencyharmonics generated by thyristor switch-on and thedesign of suppression components is based on this.This investigation has been performed in order toestablish the validity of this assumption, since it isbelieved that there may be a number of perhapsseparate sources of noise in thyristor circuits. Fourwell-known circuits have been examined, bothexperimentally using a spectrum analyser and by atheoretical analysis of the waveforms to define theharmonic spectrum expected. The presence ofrandom noise, in addition to the expected harmonics,is demonstrated.

2 EXPERIMENTAL DETAILS

The four single-phase circuits investigated were asingle-thyristor half-wave rectifier, a triac a.c. con-troller with firing angle control, a thyristor full-waverectifier bridge, and a triac a.c. controller withintegral cycle control. The triac functions as twothyristors in anti-parallel, but has a single gateelectrode. The load current waveforms were ex-amined and these have the form shown in Figure 1.From the conducted interference viewpoint, thesupply current is of interest. The supply current is thesame as the load current in all circuits except therectifier bridge, in which case it has the same form asthat of the triac with firing angle control.

44 J.K. HALL

(d)

((1} Single thyristor, hall-wave rectifier.b) Variable a.c. by trioc with firing angle control.

(c) Thyristor bridge, full-wove rectifier.(d) Variable a.c. by triac with integral cycle control.

FIGURE Output waveforms for the circuitsexamined.

The basic measuring circuit is shown in Figure 2.This consists of a resistive load of low inductancesupplied from single-phase a.c. mains through thethyristor controller. In series with the load is asampling resistor of very low inductance, acrosswhich a voltage proportional to load current is taken.This is fed to a Hewlett-Packard spectrum analyser8

and an oscilloscope. This arrangement is more suit-able for study of the low frequency harmonics, sincecombined symmetrical and asymmetrical radio-frequency components are indicated. For detailedstudy of the radio-frequency voltages, the techniquesof BS 8009 are more appropriate. The complete testcircuit is installed in a screened room in order toreduce external interference.

The principle of the spectrum analyser is that thewaveform under examination is swept by a narrow-band filter (10 Hz minimum bandwidth) controlledby a variable frequency oscillator. The output isdisplayed on a storage tube whose vertical axisrepresents amplitude, and horizontal axis frequency.

Lc

Mains

No

Thyristorcircuit Sampling resitor

counter __r-t,,i o o00ooor

Frequencyanaly=er

tesistiveload

FIGURE 2 Basic measuring circuit.

A typical trace is shown in Figure 3, where theindividual harmonics at 50 Hz intervals can easily beseen. Controls on the analyser enable the bandwidthof the filter, the swept frequency limits and sweeptime to be controlled. A variable attenuator adjusts theinput signal appropriately. The frequency counter(Figure 2) gives a direct indication of the frequencyband being swept, thus enabling the specific harmonicfrequencies displayed to be interpreted. It should benoted that the spectrum analyser indicates themagnitudes of the harmonics present in the wave-form, but not their phase in relation to thefundamental.

Zdro Harmonicfrequency, frequency .(’500 HZ/C rn,)

FIGURE 3 Harmonic spectrum trace from thespectrum analyser.

THYRISTOR FREQUENCY SPECTRUM 45

3 THEORETICAL CONSIDERATIONS

The current waveforms of Figure can be resolvedinto the harmonic components present by use of thegeneral Fourier Series:-

n--cfit) Ao + E Cn sin(not. + n)

n:l

where f(t) is the waveform function under consideration,n is the harmonic order- 1,2,3

Ao is the direct componentCn is the amplitude of the nth harmonicn is the phase of the nth harmonic.

The expansion is calculated from:

Cn (An 2 + Bnwhere

fit) cos n cot d(cot)

and

fit) sin n cot d(ot)

-1 Ann tanBn

The mean or d.c. level is given by:

2r

Ao | fit) dt2n o

The constants An, Bn and Ao for each waveform areas follows:

a) Half-wave rectifier:nth harmonic of the supply frequency (n 2,3,4,...):

1" [cos(1 + n)ot cos(1 n)ot 2(-1)n]An [ + +

27r + n n n]

] [sin( + n)a sin(1 n)a]Bn=- -+n -n

d.c. component:

Ao (cos ot + 1)2r

fundamental:

[cosA2r

B1 rr--&+2n 2

where a is the firing delay angle,and ] is the peak value of the sinusoidal current.

b) Triac with firing delay:nth harmonic of the supply frequency (n 3,5,7,...):

][cos(n+l)t cos(n-1)a 2 ]An7r n+l n-1 n2-1

l[sin(n+ 1)o sin(n-1)o]n n+l n-1

Even harmonics are absent, since An Bn 0 thn 2,4,6,... during the derivation.

d.c. component:

Ao 0

fundament:

] [cos2-l]2

[ sin 2a]B12

c) Full-wave rectifier:nth harmonic of the supply frequency (n 2,4,6,...):

[cos(l+2n)a cos(1-2n)a 2 ]An + +rr l+2n 1-2n 1-4nz

[sin(1 + 2n)a sin(1 2n)a]n k i +2n 1-

Odd harmonics are absent, since An Bn 0 withn 3,5,7, during the derivation.

d.c. conponent:

Ao [1 + cos a]

fundamental:

A1 =B1 =0

d) Triac with &tegral-cycle control:nth harmonic of the output waveform (n 1,2,3,...T, 3T, 5T,...):

iT [ (2nrrN) ]cosAnrr(n2 T2) T

46 J.K. HALL

TABLEMeasured harmonic amplitudes (as a % of mains) with varying firing angle for the

half-wave rectifier circuit.

Firing angle a Amplitude at the stated harmonic frequency (Hz)

50 100 150 500 1000 2000(Degrees) (fundamental) (2nd) (3rd) (10th) (20th) (40th)

18 50.0 22.0 1.4 1.0 0.4 0.2054 43.0 27.0 10.0 2.4 1.0 0.4590 28.0 23.0 15.0 3.0 1.2 0.60126 11.0 10.0 9.0 2.5 1.0 0.45162 1.3 1.5 1.8 1.0 0.4 0.20

iT (2nrN)Bn sin

rr(n2 T2) T

Putting n gives the coefficients for the funda-mental frequency at the load; that is, the lowestsubharmonic of the supply frequency (= 1/T x supplyfrequency). Other coefficients are given for fre-quencies up to that of the supply voltage. The coef-ficients for the supply frequency harmonic of theload current (n T):

AT =0

^NBT I-

T

For higher frequencies:

An Bn =0

for harmonics which are even multiples of the supplyfrequency (n 2T, 4T, 6T,...).d.c. component:

Ao 0

where T is the number of supply cycles in a period ofintegral-cycle control, and N is the number of ’ON’cycles in a period of integral-cycle control. Theindividual harmonic amplitudes Cn and phases, n(when required) were calculated with the aid of acomputer for assumed values of n and firing delay aor on/off cycle ratio, as appropriate.

4 RESULTS AND DISCUSSION

It is appropriate to consider the low frequency andhigh frequency harmonic components of the currentwaveforms separately. The individual thyristor circuitsare taken in order.

a) Thyristor Half-Wave RectifierThe results of measurements of specific lowfrequency harmonics generated with the singlethyristor control are given in Table I. They are shownas a function of firing angle and it is apparent that theharmonics are a maximum with a firing delay of 90A detailed representation of the harmonics present upto 1900 Hz with a firing delay of 90 is shown inFigure 4. Both measured and computed values aregiven; it can be seen that these agree very well.

Measurements of the high frequency componentsup to 300 kHz were made. the spectrum analyserindicated the presence of random noise between thepredicted lines of the harmonic spectrum. Table IIsummarises the measured amplitudes of the har-monics at 50 kHz and 100 kHz, together with theinterharmonic noise level near these frequencies, bothas a function of firing angle. As is to be expectedfrom the low frequency harmonic results, the highfrequency harmonics have a maximum amplitudewith the firing angle set at 90 However, the same istrue of the noise, within experimental error, thoughthe effect is not so pronounced. Table III showsmeasurements of harmonics and noise up to the

TABLE IIDependence of high frequency harmonics and noise on firing

angle for the half-wave rectifier circuit.(Values in uV across a ohm sampling resistor; 0.7 V obtained

with full mains applied)

Firing angle At frequency 50 kHz At frequency 100 kHz(Degrees) Harmonics Noise Harmonics Noise

18 20 8 2 254 60 15 20 890 80 15 30 8126 70 15 25 10162 35 8 12 5


I00

FIGURE 4

80-

60-

40-

o 200

xl

s6o ,ooo ,.bo doo

Amplitude values x I0Harmonic frequency (Hz

Measured on the Spectrum AnalyserComputed values using Fourier Analysis

Low-frequency harmonics from the half-waverectifier ckcuit (90 firing delay).

TABLE IIIMeasured high frequency harmonic amplitudes and noise for

the half-wave rectifier circuit with 90 firing delay.(Amplitudes in uV across a 5 ohm sampling resistor:

3.7V obtained with full mains applied).

Frequency Harmonic Harmonic Noise(kHz) order amplitude amplitude

10 200 4000 10030 600 1000 3060 1200 300 25100 2000 150 20130 2600 110 20160 3200 70 20200 4000 50 15230 4600 40 15260 5200 0 10300 6000 10

highest frequencies considered. Both harmonics andnoise decrease with increasing harmonic order,though the noise decreases at a much lesser rate. Atabout 300 kHz the harmonic amplitudes are such thatthey cannot be distinguished from the noise.

b) Triac with Firing DelayMeasurements similar to those made with the singlethyristor were repeated for the triac a.c. controllerand the results are shown in Tables IV and V. TableIV demonstrates again that the harmonic amplitudesare a maximum with 90 firing delay. As predicted bythe Fourier Analysis, only odd harmonics are presentowing to the symmetry of positive and negativehalf-cycles (Figure b). Table V again illustrates thedecreasing harmonic and noise amplitudes with in-creasing harmonic frequency and the merging of theharmonics into the noise around 300 kHz.

TABLE IVMeasured harmonic amplitudes (as a % of mains) with varying firing angle for the

triac circuit.

Firing angle Amplitude at the stated harmonic frequency <Hz)

50 150 250 550 1050 2050(Degrees) (fundamental) (3rd) (5th) (1 lth) (21st) (4 lst)

18 98 4 3.0 2.0 1.0 0.454 90 18 10.0 3.5 1.8 1.090 58 30 10.0 9.0 3.5 1.2126 48 18 10.0 4.5 1.5 1.0162 2 2 2.5 1.9 0.5 0.4

48 J.K. HALL

TABLE VMeasured high frequency harmonic amplitudes and noisefor the triac circuit with 90 firing delay. (Amplitudes intV across a 5 ohm sampling resistor; 3.7 V obtained withfull mains applied).

Frequency Approx. harmonic Harmonic Noise(kHz) order amplitude amplitude

10 200 3500 10030 600 800 5060 1200 250 40100 2000 140 40130 2600 80 40160 3200 80 30200 4000 50 25230 4600 30 25260 5200 20

c) Thyristor Full-Wave RectifierThe low-order harmonics measured in the d.c. loadcurrent waveforms (Figure c) are shown in Table V1as a function of firing angle. Only even harmonics ofthe supply frequency are present, 100 Hz being thefundamental ripple frequency. The harmonics of thisripple frequency exhibit their maxima at 90 firingdelay. As mentioned earlier, the a.c. line currentdrawn has the same waveform as is produced by triaccontrol (Figure lb), so that Tables IV and V providethe relevant information for the rectifier supplycurrent.d) Triac with Integral-Cycle Control.The zero-voltage switching of integral-cycle controlresults in the absence of high frequency harmonics,and herein lies the advantage of the method. This isillustrated in Figure 5 which shows results obtainedwith equal on and off periods. Change in the ratioon/off cycles will produce a variation in harmonicamplitudes, but the general pattern of a predomi-nance of low order harmonics and subharmonics of thesupply frequency is well demonstrated. The presence

ofsubharmonics is disadvantageous with loads of a lowthermal time constant, for which this method ofcontrol may be inappropriate. No measurements havebeen taken at the high frequency end ofthe spectrum.

Only measured results have been quoted in mostcases since Figure 4 shows that these agree fairlyclosely with those computed from the FourierAnalysis. An infinite rate of current rise at thyristorturn-on with firing angle control has been assumedfor the analysis though this is not attained in practice.For this reason the correlation is less good at thehigher frequencies. The presence of the interharmonicnoise with firing angle control is the most outstandingfeature observed. The fact that this exceeds theharmonics at frequencies above about 260 kHz is verysignificant. Tests with the single thyristor in circuit,with the triggering signal removed, and carrying d.c.revealed only minimal noise, showing that most ofthe noise is generated by the thyristor control andnot the sampling resistor or other peripheral equip-ment.

5 CONCLUSIONS

The measurements have confirmed the presence ofharmonics in the load currents of the thyristorcircuits examined and have defined their pattern. Withfiring angle control the harmonic amplitudes decreasesharply with increasing harmonic frequency but theyextend to very high harmonic orders or around 6000.The amplitudes of the harmonics measured are amaximum for a firing delay angle of around 90,though this does not necessarily apply to allthe harmonics present.1 Integral cycle controlproduces only low-order harmonics and sub-harmonics. Computed results have not been given inevery case as correlation with measurements is good,though this is less so at the highest frequencies. Withfiring angle control, apparently random, inter-

TABLE VIMeasured harmonic amplitudes (as a % of mains) with varying firing angle

for the full-wave bridge circuit.

Firing angle a Amplitude at the stated harmonic frequency (Hz)

100 200 300 500 1000 2000(Degrees) (2nd) (4th) (6th) (10th) (20th) (40th)

18 50.0 12.0 6.0 2.0 1.5 0.654 60.0 12.0 11.0 5.5 3.5 1.490 45.0 20.0 12.0 7.0 4.0 1.5126 18.0 15.0 11.0 4.0 2.5 1.5162 2.5 2.5 2.5 2.0 1.2 0.5


FIGURE 5

I00

20 40 60Illlllllllll[lllllil

;20 2haHarmonic frequency. (Hz)

Harmonics from the integral-cycle a.c. control circuit (25:25 cycles on/off ratio).

harmonic noise is present, the harmonics fallingbelow this noise level at frequencies of approximately250 kHz-300 kHz, for the resistive load used. Thenoise amplitude decreases with increasing frequencyand is a maximum with 90 firing delay. Investigationinto the causes of noise generated by thyristorcontrol is continuing.

ACKNOWLEDGEMENT

Acknowledgement is made of the experimental facilitiesprovided by the Department of Electronic and ElectricalEngineering, Loughborough University of Technology. Theadvice and encouragement of Professor D. S. Campbell isgreatly appreciated.

REFERENCES

F.E. Gentry et al., Semiconductor Controlled Rectifiers,(Prentice-Hall 1964).

2 J.R. Taylor et al., Electronic Engineering, 43, 37-41(August, 1971).

3 D.W. Matthias, IEEE Electromagnetic CompatibilitySymposium Record, 29-34 (June, 1969).

4 A. A. Collie, lEE Electronics and Power, 18, 19-22(January, 1972).

5 SCR Manual (5th Edition) General Electric Co. Chap.17.

6 P.J. Harrop, Electron, No. 19, 13-14 (11 January,1973).

7 H.P. Kaiserworth, Siemens Electronics ComponentBulletin, VII, 49-52 (1972).

8 R. C. Keiter, Hewlett--Packard Journal 23, (1), 4-9(September, 1971).

9 BS800, Parts and 3, 1972.10 R. Smith, Electronic Engineering, 36, (442) 832-837

(1964).

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2010

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal ofEngineeringVolume 2014

Submit your manuscripts athttp://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


frequency spectrum by thyristordownloads.hindawi.com/journals/apec/1974/912162.pdfthis investigation...

Documents